Although appealing to more refined tastes, art as a collectible has not always performed so profitably. During 2003, Sotheby’s s

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Although appealing to more refined tastes, art as a collectible has not always performed so profitably. During 2003, Sotheby’s s

old the Edgar Degas bronze sculpture Petite Danseuse de Quatorze Ans at auction for a price of $10,311,500. Unfortunately for the previous owner, he had purchased it in 1999 at a price of $12,377,500. What was his annual rate of return on this sculpture? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

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1 answer:

Nady [2.9K] · Answer 1 · 2026-02-22T23:11:20+03:00

Response:

The yearly return on the investment in this sculpture is -4.46%.

Details:

Let PV represent the investment amount, while FV is the value after t periods.

FV = PV(1+r)^t

(1+r)^t = FV/PV

1 + r = (FV/PV)^(1/t)

r = (FV/PV)^(1/t) - 1

Here, t is the duration from 1999 to 2003, so t = 2003 - 1999 = 4 years.

FV is $10,311,500.

PV is $12,377,500.

r = ($10,311,500/$12,377,500)^(1/4) - 1

r = -0.0446

Consequently, his yearly rate of return on the sculpture is -4.46%.